Determination of structure factor phases.

Macromolecular structure factor phases may either be determined by some variation of heavy atom replacement or by molecular replacement (MR). As MR was not successful in this project we shall be concerned here only with heavy atom based phasing procedures. Heavy atoms can be introduced into the protein crystal either by soaking the crystal in solutions containing heavy metals in the millimolar concentration range or by substitution of derivatised amino acids. It is often difficult to get high occupancy substitution of heavy atoms and even then the resulting crystal may not be isomorphous with the native crystal. When a successful derivative is found, there will be a difference in the intensity of the diffraction pattern between the native and derivative crystals, which is due to the bound heavy atom i.e.;

Fh ~ FpH“ Fp

Fp is the structure factor corresponding to the native protein; Fpn, the structure factor corresponding to protein-heavy atom derivative; Fh, describes the structure factor of the heavy atom alone. The differences in the magnitudes of Fh and Fpn can be used in a Patterson function to locate the position of the heavy atoms.

A Patterson map is an originless vector map o f all the atoms in the unit cell. It can be calculated dirrectly from the diffraction data using just the | F | ^ terms o f each reflection as no phase information is required. The Patterson Function is defined in equation 3.

The patterson function can be regarded as a convolution of the electron density at all points xyz in the unit cell with the electron density at x+u, y+v and z+w. Peaks will be observed in the Patterson map if (u,v,w) corresponds to a vector that relates 2 atomic positions.

A difference Patterson is calculated by squaring the differences between the structure factor amplitudes for the native protein and the derivatised protein. The resulting Patterson map can be solved by either visual inspection of the Harker sections (see below) or by automated procedures such as HASSP (CCP4 1994). Harker sections are special planes that arise from the crystal symmetry (Harker D, 1936). For example in space group P6422, vectors between equivalent atoms in two molecules related by the 6 fold screw axis will lie on a plane one third along and perpendicular to the six fold axis. In the same way, the crystal two-fold axis will generate another Harker section perpendicular to the twofold passing through the origin. Harker sections contain peaks due to vectors between symmetry related heavy atoms; the position of these peaks reveal the location of the heavy atoms. Once the atomic positions are known, phases can be calculated from the native and derivative amplitudes. With just a single derivative two equally probable phases are found. This ambiguity can be resolved by using another heavy atom derivative in the MIR case (Multiple isomorphous replacement) or by including anomalous scattering information; this is often referred to as MIRas (MIR with anomalous scattering).

2.4

Muitiwavelength Anomalous Dispersion (MAD).

Another method of phase determination is by the Multiwavelength Anomalous Dispersion (MAD) technique. This is a variation of the heavy atom replacement method but unlike MIR, all the phasing information can be obtained from a single

crystal. This method was used in this work for phase determination and is briefly described in the following paragraphs. MAD phasing is reliant on the two sets of information that arise from the dispersive and the anomalous contributions to anomalous scattering. The MAD dispersive signal is obtained from changes in the real component o f the scattering from the anomalous centre that arises between the same reflections measured at different wavelengths. The anomalous signal manifests itself as the Bijvoet differences between Friedel mates.

The theoretical possibility of MAD was understood long before it became a practical technique. With the emergence of tuneable synchrotron sources, which can provide very intense and finely focused monochromatic X-rays, methodologies were developed and successfully used by Hendrickson (1991) and others (Smith J L, 1991) to overcome the critical phase problem in macromolecular crystallography. The advantages o f MAD over isomorphous replacement (MIR, SIR) methods include the removal of non-isomorphism as all the necessary data can be collected from a single crystal. MAD offers better phasing potential at high resolution as unlike scattering from a heavy atom derivatised crystal, the anomalous scattering intensity does not fall off as a function of the resolution.

To carry out a MAD experiment the protein being studied must contain an atom that exhibits significant anomalous scattering at a wavelength between 0.8-1.8Â. As such, there are only a few atoms that can be exploited by MAD for protein phase determination. Examples are given in table 3, which shows the more commonly used heavy atoms in protein crystallography. Elements that have measurable L edges would be the most useful in MAD as a large anomalous signal could be attained, however, it is not always possible to use these atoms because they are not normally found as intrinsic atoms in proteins. These atoms can be added to the crystals as in isomorphous replacement (MIR) but as such, are prone to the problems associated

with MIR except for isomorphism (although it is often said that there are three problems with MIR; lack of isomorphism, lack of isomorphism and lack of isomorphism). The anomalous component of the atoms commonly found in macromolecules (e.g. H, C, O, N, S, and P) is negligible and does not affect the experiment (Hendrickson et al., 1991).

Table 3 Examples of atoms that could be used for MAD phasing.

Atomic properties Absorption edges (A)

Element Atomic No. K L ' \ }

Co 25 1.60815 13.343 15.543 15.8314 Zn 30 1.28340 10.330 11.8395 12.1055 Se 34 0.97974 7.467 8.4212 8.6624 Cd 48 0.46407 3.08490 3.32570 3.50470 Ft 78 0.15818 0.89310 0.93414 1.07230 Hg 80 0.14923 0.83530 0.87220 1.00910

This table was reproduced from H elliwell (1992).

Anomalous scattering is dependent on wavelength and thus, only results when the energy o f the X-ray beam is near the absorbance edge of the anomalous scatterer to be exploited. Often the signal from anomalous scattering is quite small i.e.; the difference between the overall intensity of normal data set and a data set with an anomalous component may only be a few percent. Therefore it is important to collect data of appropriately high quality.

In normal situations, i.e., at an energy above or below the absorption edge. X-rays are scattered ‘normally’; that is, the electrons behave as free entities and scatter the X-

rays with a constant phase change of 180°. At the absorbance edge o f a suitable anomalous scatterer, part of the energy of the X-ray is scattered normally, and part of it is absorbed by the atom. This absorption results in the transition o f inner shell electrons to a higher energy orbital in the continuum. However, the transferred electron still behaves like an inner shell electron and act as a secondary scattering source; this leads to an anomalous scattering increment /Sf to the normal scattering / ° . When the electron is ejected from the inner shell to higher energy state, another electron falls back to fill the void. In the process of dropping to the lower energy level, the electron emits the excess energy as fluorescence.

Normal scattering (f°) is real and independent of wavelength but decreases as a function o f resolution. In the presence of an anomalous scatterer, normal scattering is composed of the scattering from the protein (/°p ) and the anomalous scattering atom ( f °a); thus total normal scattering / ° is composed o f / °p+ / °a. The anomalous scatterer also has an anomalous scattering component, A f that is complex. A f is dependent on wavelength and largely independent of resolution. A / is composed of / ' (dispersive signal) and /" (anomalous signal), the real and the imaginary parts respectively. These two are orthogonal to each other (figure 13). Thus total scattering F is given by equation 4.

F =/°(p+a) + / ' + i / " . [4]

As a result of the anomalous component, the structure factor amplitudes are no longer equal for reflections related by Friedel’s symmetry i.e.; reflections F(h, k, i) ^ F(_h, -k, -i). This difference between Friedel pairs is called the Bijvoet difference.

Figure 13 MAD phasing. (j)p - p h a se of - p h a se of Fh - p h a se o f F f - p h a se of Fp

- normal scattering from the a n o m o lo u s scatterer - total scattering including the a n o m a lo u s co m p o n e n t - total normal scattering - scattering from protein

X2 ^3

- far from the absorption e d g e of the a n o m a lo u s scatterer

- r maximum - f minimum

T h e p o sitio n of th e a n o m a lo u s sc a tte r in g a tom c a n b e a p p r o x im a te ly d e te r m in e d from a n a n o m a l o u s a n d d i s p e r s iv e d if f e r e n c e P a t t e r s o n . O n c e th is is k n o w n , th e m a g n itu d e of F*, p h a s e (#* a n d /' a n d /" at Xg an d A.3 c a n b e c a lc u la te d . T h e m a g n itu d e of Fh at X2 a n d X3 c a n b e u s e d to draw p h a s e c ir c le s to d e te r m in e (|)h.